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Since the Drucker–Prager yield surface is a smooth version of the Mohr–Coulomb yield surface, it is often expressed in terms of the cohesion and the angle of internal friction that are used to describe the Mohr–Coulomb yield surface. [2]
The quadratic Hill yield criterion [1] has the form : + + + + + = . Here F, G, H, L, M, N are constants that have to be determined experimentally and are the stresses. The quadratic Hill yield criterion depends only on the deviatoric stresses and is pressure independent.
The two plastic limit theorems apply to any elastic-perfectly plastic body or assemblage of bodies. Lower limit theorem: If an equilibrium distribution of stress can be found which balances the applied load and nowhere violates the yield criterion, the body (or bodies) will not fail, or will be just at the point of failure.
Greenwood and Williamson [31] defined a dimensionless parameter called the plasticity index that could be used to determine whether contact would be elastic or plastic. The Greenwood-Williamson model requires knowledge of two statistically dependent quantities; the standard deviation of the surface roughness and the curvature of the asperity peaks.
However, the possibility of negative values of and the resulting imaginary makes the use of these quantities problematic in practice. Another related set of widely used invariants is ( ξ , ρ , θ {\displaystyle \xi ,\rho ,\theta \,} ) which describe a cylindrical coordinate system (the Haigh–Westergaard coordinates).
Mode III is a tearing (antiplane shear) mode where the crack surfaces move relative to one another and parallel to the leading edge of the crack. Mode I is the most common load type encountered in engineering design. Different subscripts are used to designate the stress intensity factor for the three different modes.
Furthermore, it is a failure mode independent criterion, as it does not predict the way in which the material will fail, as opposed to mode-dependent criteria such as the Hashin criterion, or the Puck failure criterion. This can be important as some types of failure can be more critical than others.
Which can be expressed as: [2] = where m is known as the Schmid factor = Both factors τ and σ are measured in stress units, which is calculated the same way as pressure (force divided by area). φ and λ are angles.